Method and system for determining source signatures after source ghost removal

ABSTRACT

Seismic data are acquired using a seismic source comprising a plurality of seismic sub-sources disposed in a body of water at a plurality of depths and activated with different time delays. Far-field signatures are determined for the plurality of seismic sub-sources at each of the plurality of depths. A composite ghost-free far-field signature of the seismic source is determined from the far-field signatures for the plurality of seismic sub-sources at each of the plurality of depths and different time delays. A source response is removed from the seismic data using the far-field signatures of the seismic source

CROSS-REFERENCE TO RELATED APPLICATION

This application is a divisional of application Ser. No. 13/367,787,filed Feb. 7, 2012.

BACKGROUND

In the oil and gas industry, geophysical prospecting is commonly used toaid in the search for and evaluation of subsurface earth formations.Geophysical prospecting techniques yield knowledge of the subsurfacestructure of the earth, which is useful for finding and extractingvaluable mineral resources, particularly hydrocarbon deposits such asoil and natural gas. A well-known technique of geophysical prospectingis a seismic survey. In a land-based seismic survey, a seismic signal isgenerated on or near the earth's surface and then travels downward intothe subsurface of the earth. In a marine seismic survey, the seismicsignal may also travel downward through a body of water overlying thesubsurface of the earth. Seismic energy sources are used to generate theseismic signal which, after propagating into the earth, is at leastpartially reflected by subsurface seismic reflectors. Such seismicreflectors typically are interfaces between subterranean formationshaving different elastic properties, specifically sound wave velocityand rock density, which lead to differences in acoustic impedance at theinterfaces. The reflected seismic energy is detected by seismic sensors(also called seismic receivers) at or near the surface of the earth, inan overlying body of water, or at known depths in boreholes. The seismicsensors generate signals, typically electrical or optical, from thedetected seismic energy, which are recorded for further processing.

The appropriate seismic sources for generating the seismic signal inland seismic surveys may include explosives or vibrators. Marine seismicsurveys typically employ a submerged seismic source towed by a ship andperiodically activated to generate an acoustic wavefield. The seismicsource generating the wavefield may be of several types, including asmall explosive charge, an electric spark or arc, a marine vibrator,and, typically, a gun. The seismic source gun may be a water gun, avapor gun, and, most typically, an air gun. Typically, a marine seismicsource consists not of a single source element, but of aspatially-distributed array of source elements. This arrangement isparticularly true for air guns, currently the most common form of marineseismic source.

The appropriate types of seismic sensors typically include particlevelocity sensors, particularly in land surveys, and water pressuresensors, particularly in marine surveys. Sometimes particle displacementsensors, particle acceleration sensors, or pressure gradient sensors areused in place of or in addition to particle velocity sensors. Particlevelocity sensors and water pressure sensors are commonly known in theart as geophones and hydrophones, respectively. Seismic sensors may bedeployed by themselves, but are more commonly deployed in sensor arrays.Additionally, pressure sensors and particular motion sensors may bedeployed together in a marine survey, collocated in pairs or pairs ofarrays.

In a typical marine seismic survey, a seismic survey vessel travels onthe water surface, typically at about 5 knots, and contains seismicacquisition equipment, such as navigation control, seismic sourcecontrol, seismic sensor control, and recording equipment. The seismicsource control equipment causes a seismic source towed in the body ofwater by the seismic vessel to actuate at selected times (the activationcommonly known as a “shot”). Seismic streamers, also called seismiccables, are elongate cable-like structures towed in the body of water bythe seismic survey vessel that tows the seismic source or by anotherseismic survey ship. Typically, a plurality of seismic streamers aretowed behind a seismic vessel. The seismic streamers contain sensors todetect the reflected wavefields initiated by the seismic source andreturning from reflective interfaces.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention and its advantages may be more easily understood byreference to the following detailed description and the attacheddrawings, in which:

FIG. 1 is a diagram of a system for acquiring seismic data that can beused with seismic data processing methods according to the invention;

FIG. 2 is a flowchart illustrating an example embodiment of a method formapping the earth's geology;

FIG. 3 is a flowchart illustrating an example embodiment of a method fordetermining the far-field signatures;

FIG. 4 is a flowchart illustrating an example embodiment of a method forremoving the source response from the seismic data;

FIG. 5 is a flowchart illustrating an example embodiment of a method forremoving the receiver ghost from the seismic data; and

FIG. 6 is a diagram illustrating, by way of example, one of manydifferent types of computer systems that can be used with seismic dataprocessing methods according to the invention.

While the invention will be described in connection with its preferredembodiments, it will be understood that the invention is not limited tothese. On the contrary, the invention is intended to cover allalternatives, modifications, and equivalents that may be included withinthe scope of the invention, as defined by the appended claims.

DETAILED DESCRIPTION

FIG. 1 is a diagram of an exemplary system for acquiring seismic datathat can be used with seismic data processing methods according to theinvention. In various embodiments, a single seismic sensor cable (alsocalled a seismic streamer) or a single ocean bottom cable are shown forsimplicity of illustration. This illustration of one cable is only meantto more clearly demonstrate principles of the invention and is notintended as a limitation of the invention.

In FIG. 1, the seismic acquisition system is designated generally as100. A seismic vessel 101 is disposed in a body of water 102 and carriesequipment 103 for navigation, seismic source control, and seismic sensorrecording. The seismic vessel 101 or another service vessel (not shown)tows a seismic source 104 through the body of water 102 below thesurface 105 of the water. The seismic source 104 comprises anyappropriate type of source, typically in arrays. The seismic source 104illustrated in FIG. 1 comprises a plurality of sub-sources 104,positioned at different depths. Two sub-sources are shown, but theconfiguration of seismic sub-sources 104 illustrated in the seismicacquisition system 100 is not intended to be a limitation of theinvention.

In one embodiment, the seismic vessel 101 or another service vessel (notshown) tows a seismic streamer 106 through the body of water 102. Theseismic streamer 106 comprises seismic sensors 107 at spaced apartpositions along the seismic streamer 106, so that the seismic streamer106 containing the seismic sensors 107 is disposed in the body of water102. The seismic sensors 107 are typically pressure sensors, such ashydrophones. In another embodiment, the seismic streamer 106 comprises adual-sensor streamer, in which the seismic sensors 107 comprise pairs ofcollocated pressure and particle motion sensors. The particle motionsensors are typically particle velocity sensors, such as geophones, oraccelerometers. The seismic sensors 107 typically comprise arrays ofsensors at each spaced apart position. An alternative to having thepressure and particle motion sensors co-located is to have sufficientspatial density of sensors so that the respective wavefields recorded bythe pressure and particle motion sensors can be interpolated orextrapolated to produce the two wavefield signals at the same location.

In another embodiment, the seismic vessel 101 or another service vessel(not shown) disposes an ocean bottom cable 108 on the water bottom 109.The ocean bottom cable 108 also comprises seismic sensors 107 at spacedapart positions along the cable, also typically in arrays of sensors ateach spaced apart position. The seismic sensors 107 in the ocean bottomsensor 108 can also comprise pairs of pressure and particle motionsensors. In yet another embodiment, both seismic streamers 106 and oceanbottom cable 108 are employed. The type of sensors illustrated in theseismic acquisition system 100 is not intended to be a limitation of theinvention. For example, in other embodiments, discrete seismic sensors107 located at ocean bottom nodes (not shown) could be included in theseismic acquisition system 100.

When the seismic source 104 is activated, acoustic energy travelsdownwardly, at 110, through the body of water 102 and the water bottom109 to layer boundaries, such as 111 and 112, surrounding a subterraneanformation layer, such as 113. A portion of the acoustic energy isreflected from the layer boundary at 111 and travels upwardly, at 114.The upwardly traveling acoustic energy 114 is detected at seismicsensors 107 on the ocean bottom cable 108 or the seismic streamer 106.The upwardly traveling acoustic energy continues upward, at 115, untilreflecting off the water surface 105 and then travels downwardly again,at 116. The downwardly traveling acoustic energy 116 may be detectedagain by seismic sensors 107 on the seismic streamer 106 or the oceanbottom cable 108, resulting in a ghost signal. The acoustic energydetected at the seismic sensors 107 may be recorded onto any type ofappropriate storage media at any location, such as, but not restrictedto, at the seismic streamer 106 or the ocean bottom cable 108, on theseismic vessel 101 or another service vessel, or onshore.

As shown above in FIG. 1, marine seismic exploration typically employs asubmerged seismic source 104 towed by a ship and periodically activatedto generate an acoustic wavefield (the shot). The wavefield may begenerated by a small explosive charge, an electric spark or arc, avibrator, or, typically, a gun. The gun may be a water gun, vapor gun,or, most typically, an airgun. Each airgun contains a volume of airtypically compressed to about 2000 psi (pounds per square inch) or more.An airgun abruptly releases its compressed air to create an air bubble,leading to an expanding sound wave in the water. The resulting wavefront propagates downwardly into the earth beneath the water, reflectsfrom subterranean earth layers, and returns upwardly toward the watersurface.

When a seismic source is triggered, it produces a complex outputpressure pulse in the water. In an idealized situation in which theseismic source is a point source, such as a single airgun, and there isno sea surface, the emitted wave front is independent of direction anddistance, except for spherical spreading. Converted to an electricalsignal, the output pulse of an airgun would consist of a short wavetrain whose envelope displays an initial short, fast, positive rise inamplitude followed by several rapidly-decaying oscillations. Therecorded wave train is called the signature of the seismic source.

In practice, a sea surface exists and is typically only meters away fromthe seismic source. The acoustic wave generated by the seismic sourceradiates by spherical spreading in all directions such that there is adownwardly traveling component as well as an upwardly travelingcomponent. The water-air interface at the sea surface has a reflectioncoefficient typically close to a value of −1. The upwardly travelingcomponent of the acoustic wave is reflected by the water surface and isreversed in polarity to become another downgoing component. Thisadditional downgoing component is generally referred to as a “ghost”.The ghost interferes with the direct wave to complicate the sourcesignature.

Typically, a seismic source consists not of a single source element, butof a spatially-distributed array of source elements that generate directarrivals plus the ghost components. This is particularly true ofairguns, currently the most common form of marine seismic source. Thespatial dimensions of an array of seismic source elements may becomparable to the wavelengths of the acoustic waves themselves withinthe useful seismic frequency passband. Thus, there is no single sourcesignature for an array. Rather, the source signature of an array in thenear-field becomes a continuous function of both direction and distance.At distances large compared with the array dimensions, the dependence ondistance of the source signature in any particular direction becomesnegligible. This region is called the far-field and the source signaturehere is called the far-field signature. In particular, the far-fieldsignature is the wavelet traveling vertically downwards from the sourcearray, including the sea surface ghost reflection (source and receiverghosts), and at a large enough distance that the shape of the wavelet issubstantially invariant with increasing distance. For arrays of airguns,which typically extend over spatial dimensions of about 20 meters by 20meters, the distance to the far-field is on the order of 250 meters.

In reality, the source signature at a distance does vary with take-offangle from the seismic source. Nonetheless, the far-field signaturedefined above is representative of the source response in conventionalseismic data to a first-order approximation. This vertical far-fieldsignature is useful for seismic data processing in order to sharpen thewavelet and correct the phase response, normally to zero- orminimum-phase. In particular, this far-field signature is used fordeconvolving the source response. Alternatively, a more complexdirectional deconvolution of the source response could be used. Forexample, source signatures at different emission angles can becalculated by summing notional source signatures with appropriate timeshifts. One method for calculating the notional source signatures is touse near-field measurements from the seismic source array. Typically,there is one near-field hydrophone per source element. The measurablesignature p_(j)(t) at the j^(th) hydrophone is given by:

$\begin{matrix}{{{p_{j}(t)} = {\sum\limits_{i = 1}^{n}\;{( \frac{1}{r_{ij} - {tv}_{ij}} ){p_{i}^{\prime}( t_{ij} )}}}},{{{for}\mspace{14mu} j} = 1},2,\ldots\mspace{14mu},{n.}} & (1)\end{matrix}$Here, r_(ij) is the distance between the i^(th) seismic source-generatedair bubble and the j^(th) hydrophone, v_(ij) is a closing relativevelocity between the i^(th) bubble and the j^(th) hydrophone, p′_(i) isa weighted unknown signature, and t_(ij) is given by:

$\begin{matrix}{t_{ij} = {t - {\frac{r_{ij} - 1}{c}.}}} & (2)\end{matrix}$Other methods exist in the prior art for determining the far-fieldsource signature, s_(ng)(t), so that it can be removed from the seismicwavelet, w(t).

The notional source method is first described in Ziolkowski, A., Parkes,G., Hatton, L., and Haugland, T., “The signature of an airgun array:Computation from near-field measurements including interactions”,Geophysics, Vol. 47, No. 10 (October 1982), pp. 1413-1421. Thecalculation of far-field signatures normally includes the source ghost,and possibly also the receiver ghost, since these ghosts are anintrinsic part of the seismic wavelet that appears in the seismic data.A notional source signature is a signature that describes the wavefieldemitted by a single source element (gun or cluster) of an array ofmarine seismic sources. The notional source signature cannot be measureddirectly because any hydrophone placed near any particular sourceelement will also record contributions from the wavefields of all thesurrounding source elements along with their ghosts. However, thenotional source can be derived from a suitable grid of hydrophonemeasurements.

The far-field signature, or its equivalent, can be determined by anumber of other methods also. For example, in a second exemplaryembodiment, the vertically travelling far-field signature is directlymeasured with a far-field hydrophone. This method requires positioningthe sensor (hydrophone) the required distance from the seismic source.The far-field method often requires moving the seismic survey vesselsand equipment to deeper waters to make the far-field measurements. In athird exemplary embodiment, the far-field signature can be modeled fromavailable data. This description of several methods is not intended tolimit the invention.

In one embodiment associated with the invention, the seismic sourcecomprises a plurality of seismic sub-sources disposed in a body of waterat a plurality of different depths and activated with different relativetime delays. In this embodiment, the source response deconvolutionhandles the source ghost separately. Thus, a ghost-free far-fieldsignature is required. This signature is equivalent to combining aplurality of ghost-free far-field signatures into a composite ghost-freefar-field signature. This result is accomplished in this embodiment byapplying de-ghosting equations to the plurality of far-field signaturesfor the plurality of sub-sources. This de-ghosting effectivelysynchronizes and merges the seismic data from the individual sub-sourcesinto a composite of ghost-free far-field signatures of the sub-sources,merged by processing through the de-ghosting equations. The result isthe composite ghost-free far-field signature of the seismic source thatis used in this embodiment to deconvolve the source response.

A seismic source configuration can be employed in which multiplesub-sources within a seismic source are deployed at different depths.The two-depth arrangement is known as an “over/under” configuration. Thesource ghost may be removed, in one example embodiment, using the methoddescribed in Posthumus, B. [1993], “Deghosting of twin streamerconfiguration”, Geophysical Prospecting, vol. 41, pp. 267-286. ThePosthumus method was originally described for over/under streamers, butit is equally applicable to over/under sources.

Using the Posthumus method, the wave field W(ω) without the source ghostcan be calculated by the following equation in the frequency domain:

$\begin{matrix}{{W(\omega)} = {\frac{0_{1}(\omega){G_{1}(\omega)}*{+ 0_{2}}(\omega){G_{2}(\omega)}*}{{{G_{1}(\omega)}}^{2} + {{G_{2}(\omega)}}^{2}}.}} & (3)\end{matrix}$Here 0₁(ω) is the recorded signal corrected for the actual actuationtime of the first set of sub-sources at one depth with respect toinitiation of recording (time t=0) in the shot record, 0₂(ω) is therecorded signal corrected for the actual actuation time of the secondset of sub-sources at another depth with respect to initiation ofrecording (time t=0) in the shot source and compensating for its beingcloser to the reflectors than the first set of sub-sources, G₁(ω) is thesource ghost for the first set of sub-sources, G₂(ω) is the source ghostfor the second set of sub-sources, and a superscript asterisk “*”designates conjugation.

In this example embodiment, the source ghost operator, g₁(t), for thefirst set of seismic sub-sources may be defined in the time domain asfollows:

$\begin{matrix}{{{g_{1}(t)} = {{\delta(t)} - {\delta( {t - {2\; d_{1}\frac{\cos\;(\alpha)}{c}}} )}}},} & (4)\end{matrix}$and similarly, the source ghost operator, g₂(t), for the second set ofseismic sub-sources may be defined as

$\begin{matrix}{{g_{2}(t)} = {{\delta(t)} - {{\delta( {t - {2\; d_{2}\frac{\cos\;(\alpha)}{c}}} )}.}}} & (5)\end{matrix}$Here, d₁ is the operating depth of the first set of sub-sources; d₂ isthe operating depth of the second set of sub-sources; α is the emissionangle of the energy propagation from the source, relative to vertical;and δ is the Dirac delta operator.

The invention, however, is not limited to just two depths. In the moregeneral case, the seismic sources comprise a plurality of sets ofsub-sources at a plurality of different depths. Let there be N sets ofsub-sources, with each set comprising seismic sub-sources at the samedepth. Then, the wavefield W(ω) without the source ghost can becalculated by the following in the frequency domain:

$\begin{matrix}{{W(\omega)} = {\frac{\sum\limits_{i = 1}^{N}\;{{O_{i}(\omega)}{G_{i}(\omega)}*}}{\sum\limits_{i = 1}^{N}\;{{G_{i}(\omega)}}^{2}}.}} & (6)\end{matrix}$Here, now, O_(i)(ω) is the recorded signal corrected for the actuationtime of the i^(th) set of sub-sources at the i^(th) depth and G_(i)(ω)is the source ghost for the i^(th) set of sub-sources. Then the sourceghost operator, g_(i)(t), for the i^(th) set of seismic sources may bedefined in the time domain as follows:

$\begin{matrix}{{{g_{i}(t)} = {{\delta(t)} - {\delta( {i - {2\; d_{i}\frac{\cos\;(\alpha)}{c}}} )}}},} & (7)\end{matrix}$for i=1, 2, . . . , N, where d_(i) is the operating depth of the i^(th)set of sources.

If the Posthumus method is applied to seismic data acquired with sourcearrays or sub-source arrays at different depths, then the source ghostis removed. In addition, the seismic wavelet itself undergoes atransformation, as the wavefields from the sub-sources at the differentdepths undergo a frequency-dependent weighted summation. Therefore, theconventional far-field signature (as described above) can no longer beused in the signature deconvolution. Instead, it is necessary todetermine the transformed source signature after combining thewavefields from a plurality of sub-sources at different depths andremoving the source ghost.

An embodiment associated with the invention accomplishes thisdetermination by determining the far-field signatures of each source oreach source component of a source array towed at different depths. Eachof these far-field signatures should include the source and receiverghosts. These far-field signatures may be determined using any of themethods already known in the art, and should include the response of thereceiver system. These far-field signatures are then input to the samealgorithm that is used for removing the source ghost in the seismic dataitself. The resulting composite ghost-free far-field signature isrepresentative of the signature in the recorded seismic data aftersource ghost removal, and can be used for designing a de-signaturefilter to correct for the phase- and/or amplitude-spectrum of thesignature. The resulting far-field signature according to thisembodiment is required for proper over/under source de-signature.

The object of the employing a seismic acquisition system 100, as in FIG.1, is to map the earth's geology using the seismic data, d(t), recordedduring the seismic survey. The ideal end product would be the pureimpulse response of the earth, which can be expressed as thereflectivity series of the earth, e_(rs)(t). In reality, conventionalrecorded seismic data comprises a convolution of the reflectivity seriesof the earth, e_(rs)(t), with a seismic wavelet, w(t), plus noise, n(t):d(t)=e _(rs)(t)*w(t)+n(t),  (8)where t is time and an asterisk “*” designates convolution.

Three major terms in this seismic wavelet are the source responseitself, the source ghost, and the receiver ghost. Although this seismicwavelet is actually a function of direction, it is often approximated bythe vertically traveling far-field signature.

The seismic wavelet, w(t), comprises a combination of the variousresponses of the earth itself, the source, receiver and surfacereflections or ghosts. Once the seismic wavelet, w(t), and the noise,n(t), are determined, they can then be removed from the recorded seismicdata, d(t). The final result is a reflectivity series of the earth,e_(rs)(t), that very closely represents the ideal impulse response ofthe earth.

In one embodiment, the seismic wavelet, w(t)=w(t,x,y,z,θ,φ), can beexpressed as a convolution of operators (functions that determine thesignatures) representing the receiver ghost, g_(r)(t)=g_(r)(t,θ,φ), thesource ghost, g_(s)(t)=g_(s)(t,θ,φ), the ghost-free source systemresponse, s_(ng)(t)=s_(ng)(t,θ,φ), the earth filter response,e(t)=e(t,θ,φ), and the receiver system response, r(t)=r(t,θ,φ). Here, tis time, θ and φ are emission angles, and x, y. and z are Cartesianspatial coordinates. For simplicity of illustration, the operators willbe expressed in the time domain. Thus, in this embodiment, the recordedseismic wavelet is described as follows:w(t)=g _(r)(t)*g _(s)(t)*s _(ng)(t)*e(t)*r(t).  (9)The earth filter response, e(t), represents the frequency-dependentattenuation as the acoustic wavefield propagates through the earth.

In one embodiment, the invention is a method and a system for properlydetermining a far-field source signature for a seismic acquisitionsystem employing sources or source components at different depths andactivated with different relative time delays.

First, the far-field source signatures of the seismic sub-sources can bedetermined based on methods described above. For example, in oneexemplary embodiment, the so-called notional source signatures can becalculated either from measured data in the field or from simulatedresponses calibrated to field measurements. Such calculations are basedon the notional source method as described above. The calculations ofthe notional source signatures need to take the interaction effects ofthe source ghost into account. However, when calculating the far-fieldsignatures from the notional source signatures, the source ghost,g_(s)(t), is not included in the calculations. To derive the far-fieldsignatures for a source array in which a plurality of sub-sources aredistributed at different depths, the far-field signatures for eachseismic sub-source need to be summed through a weighted summation methodsimilar to that used for removing the source ghost in the measured data.The resultant composite ghost-free source signature can then be used asa basis for removing the response of the source.

By using a seismic acquisition system employing source arrays in whichthe sub-sources are distributed in depth, the source ghost can beremoved through a weighted summation of the sub-sources distributed indepth. One example of such a source is an “over/under source.” Forexample, in one exemplary embodiment, the Posthumus method describedabove can be used for over/under sources (instead of streamers, asdescribed in the article).

In another example embodiment, the seismic data from one set ofsub-sources is first time shifted so that the source ghost occurs at thesame time as on the other set of sub-sources. Next, the two set ofseismic data from the two sets of sub-sources are subtracted, whichremoves the source ghost. The result of the subtraction will contain anapparent ghost with a relative amplitude of −1 and a known time delay oftwice the vertical traveltime of the distance between the depths of thetwo sets of sub-sources. Thus, a deterministic deghosting filter can beconstructed and applied to compensate for the predictable amplitude andphase effects.

In yet another example embodiment, the seismic data from two sets ofsub-sources at different depths are first filtered with deterministicfilters designed to correct only for the phase effects of the sourceghost. Next, the filtered data from one set of sub-sources aretime-shifted so that events occur at the same time in the two filtereddata sets. Then the two data sets are summed to fill in the notches inthe amplitude spectra.

In yet another example embodiment, the two seismic data sets from thetwo sets of sub-sources are both summed and subtracted from each other,yielding sum and difference data sets, respectively. Next the differencedata set is integrated and scaled by ¼ times the inverse of times halfthe traveltime between the different depths for the two sets ofsub-arrays. Next, the sum data set is scaled by ¼. Then, the scaledintegrated difference data set is subtracted from the scaled sum dataset to yield the up-going wavefield.

Hence, the effects of the source ghost, g_(s)(t), can be removed fromeach of the far-field signatures in the wavelet, w(t). Other methodsexist in the prior art for determining and removing the effects of thesource ghost, g_(s)(t), from the seismic wavelet, w(t). This descriptionof several exemplary methods is not intended to limit the invention.

With a dual-sensor or multi-component towed streamer comprising bothpressure sensors and motion sensors, the up-going and down-goingwavefields can be separated through scaled or weighted summation of themeasured components. For example, in one exemplary embodiment, theup-going and down-going pressure wavefields, P_(u) and P_(d),respectively, can be calculated from the measured pressure wavefield Pand vertical velocity wavefield component V_(z) and expressed in thefrequency domain as follows:

$\begin{matrix}{{{g_{i}(t)} = {{\delta(t)} - {\delta( {i - {2\; d_{i}\;\frac{\cos(\alpha)}{c}}} )}}},{and}} & (10) \\{{{P_{u}(\omega)} = {\frac{1}{2}\lbrack {{P(\omega)} + {\frac{\rho\;\omega}{k_{z}}{V_{z}(\omega)}}} \rbrack}},} & (11)\end{matrix}$where ω is rotational frequency, ρ is water density, and k_(z) isvertical wavenumber, given by:

$\begin{matrix}{{k_{z} = \sqrt{( \frac{\omega}{c} )^{2} - k_{x}^{2} - k_{y}^{2}}},} & (12)\end{matrix}$where c is speed of sound in water and k_(x) and k_(y) are thehorizontal wavenumbers in the x (typically inline) and y (typicallycross-line) directions, respectively.

Since the up-going pressure wavefield, P_(u), contains no down-goingreflections, the receiver ghost is not present in P_(u). Hence, theeffects of the receiver ghost, g_(r)(t), can be removed from thewavelet, w₁(t), as expressed in Equation (1). At this stage, thefollowing seismic wavelet, w₂(t), is left:w ₂(t)=g _(s)(t)*s _(ng)(t)*e(t)*r(t).  (13)Other methods exist in the prior art for determining and removing theeffects of the receiver ghost, g_(r)(t), from the seismic wavelet, w(t).This description of one method is not intended to limit the invention.For example, in another exemplary embodiment, the receiver ghost,g_(r)(t), is removed using a specially designed receiver system.

FIG. 2 is a flowchart illustrating an example embodiment of a method formapping the earth's geology.

At block 20, seismic data are obtained that are acquired using a seismicsource comprising a plurality of seismic sub-sources disposed in a bodyof water at a plurality of depths and activated with different relativetime delays. Obtaining the seismic data can include acquiring data, suchas by a marine seismic survey, or retrieving previously acquired datafrom storage, such as from computer memory or other types of memorystorage devices or media.

At block 21, far-field signatures are determined for the plurality ofseismic sub-sources in block 20 at each of the plurality of depths.

At block 22, a composite ghost-free far-field signature of the seismicsource is determined from the far-field signatures from block 21 for theplurality of seismic sub-sources at each of the plurality of depths anddifferent time delays.

At block 23, a source response is removed from the seismic data fromblock 20 using the composite ghost-free far-field signature from block22 of the seismic source.

FIG. 3 is a flowchart illustrating an example embodiment of a method fordetermining the far-field signatures. FIG. 3 further describes a portionof the method in FIG. 2.

At block 30, notional source signatures are determined for the pluralityof seismic sub-sources used to record the seismic data at each of theplurality of depths; and

At block 31, a far-field signature is determined from a weightedsummation of the notional source signatures for the plurality of seismicsub-sources at each of a plurality of depths from block 30.

FIG. 4 is a flowchart illustrating an example embodiment of a method forremoving the source response from the seismic data. FIG. 4 furtherdescribes a portion of the method in FIG. 2.

At block 40, a seismic source array with a plurality of seismicsub-sources disposed at a plurality of depths and activated withdifferent relative time delays is used to record the seismic data.

At block 41, a weighted summation is applied to the far-field signaturesfrom block 21 of FIG. 2 for the plurality of seismic sub-sourcesdisposed at the plurality of depths and with different time delays fromblock 40.

FIG. 5 is a flowchart illustrating an example embodiment of a method forremoving the receiver ghost from the seismic data. FIG. 5 furtherdescribes a portion of the method in FIG. 2.

At block 50, pressure and vertical velocity components of the seismicdata are measured.

At block 51, up-going and down-going wavefields are separated using aweighted summation of the measured pressure and vertical velocitycomponents from block 50.

The seismic data obtained in performing a seismic survey, representativeof earth's subsurface, are processed to yield information relating tothe geologic structure and properties of the subsurface earth formationsin the area being surveyed. The processed seismic data are processed fordisplay and analysis of potential hydrocarbon content of thesesubterranean formations. The goal of seismic data processing is toextract from the seismic data as much information as possible regardingthe subterranean formations in order to adequately image the geologicsubsurface. In order to identify locations in the earth's subsurfacewhere there is a probability for finding petroleum accumulations, largesums of money are expended in gathering, processing, and interpretingseismic data. The process of constructing the reflector surfacesdefining the subterranean earth layers of interest from the recordedseismic data provides an image of the earth in depth or time. Aprerequisite for discovery of any oil or gas reservoir is awell-resolved seismic image of the earth's subsurface.

The image of the structure of the earth's subsurface is produced inorder to enable an interpreter to select locations with the greatestprobability of having petroleum accumulations. To verify the presence ofpetroleum, a well must be drilled. Drilling wells to determine whetherpetroleum deposits are present or not, is an extremely expensive andtime-consuming undertaking. For that reason, there is a continuing needto improve the processing and display of the seismic data, so as toproduce an image of the structure of the earth's subsurface that willimprove the ability of an interpreter, whether the interpretation ismade by a computer or a human, to assess the probability that anaccumulation of petroleum exists at a particular location in the earth'ssubsurface. The processing and display of acquired seismic datafacilitates more accurate decisions on whether and where to drill, andthereby reduces the risk of drilling dry holes.

The invention has been discussed above as a method, for illustrativepurposes only, but can also be implemented as a system. The system ofthe invention is preferably implemented by means of computers, inparticular digital computers, along with other conventional dataprocessing equipment. Such data processing equipment, well known in theart, will comprise any appropriate combination or network of computerprocessing equipment, including, but not be limited to, hardware(processors, temporary and permanent storage devices, and any otherappropriate computer processing equipment), software (operating systems,application programs, mathematics program libraries, and any otherappropriate software), connections (electrical, optical, wireless, orotherwise), and peripherals (input and output devices such as keyboards,pointing devices, and scanners; display devices such as monitors andprinters; computer readable storage media such as tapes, disks, and harddrives, and any other appropriate equipment).

In another embodiment, the invention could be implemented as the methoddescribed above, specifically carried out using a programmable computerto perform the method. In another embodiment, the invention could beimplemented as a computer program stored in a computer readable medium,with the program having logic operable to cause a programmable computerto perform the method described above. In another embodiment, theinvention could be implemented as a computer readable medium with acomputer program stored on the medium, such that the program has logicoperable to cause a programmable computer to perform the methoddescribed above.

FIG. 6 is a diagram illustrating, by way of example, one of manydifferent types of computer systems that can be used with seismic dataprocessing methods according to the invention. A central processor 60 iscoupled to user input devices, such as a keyboard 61 (wired or wireless)and a mouse 62 (wired or wireless). The processor 60 is further coupledto a display, such as a monitor 63. A computer program according to theinvention may reside on any of a number of computer readable media, suchas a disk 64 insertable into a disk drive 65 or on an internal orexternal hard drive (not shown).

It should be understood that the preceding is merely a detaileddescription of specific embodiments of this invention and that numerouschanges, modifications, and alternatives to the disclosed embodimentscan be made in accordance with the disclosure here without departingfrom the scope of the invention. The preceding description, therefore,is not meant to limit the scope of the invention. Rather, the scope ofthe invention is to be determined only by the appended claims and theirequivalents.

The invention claimed is:
 1. A system for mapping the earth's geology,comprising: a seismic source comprising a plurality of seismicsub-sources disposed in a body of water at a plurality of depths andactivated with different time delays, seismic sensors disposed in thebody of water to detect seismic energy reflected from the earth'ssubsurface in response to seismic signals generated by the seismicsource and record the seismic energy as seismic data in a memory storagedevice; and a programmable computer used to perform at least thefollowing: determining far-field signatures for the plurality of seismicsub-sources at each of the plurality of depths; determining a compositeghost-free far-field signature of the seismic source from the far-fieldsignatures for the plurality of seismic sub-sources at each of theplurality of depths and different time delays; and removing a sourceresponse from the seismic data using the composite ghost-free far-fieldsignature of the seismic source.
 2. The system of claim 1, wherein thedetermining far-field signatures for the plurality of seismicsub-sources at each of the plurality of depths comprises: determiningnotional source signatures for the plurality of seismic sub-sources ateach of the plurality of depths; and determining a far-field signaturefrom a weighted summation of the notional source signatures.
 3. Thesystem of claim 1, wherein the determining far-field signatures for theplurality of seismic sub-sources at each of the plurality of depthscomprises: measuring the far-field signatures for the plurality ofseismic sub-sources at each of the plurality of depths.
 4. The system ofclaim 1, wherein the determining far-field signatures for the pluralityof seismic sub-sources at each of the plurality of depths comprises:modeling the far-field signatures for the plurality of seismicsub-sources at each of the plurality of depths.
 5. The system of claim1, wherein determining the composite ghost-free far field signature ofthe seismic source from the far-field signatures for the plurality ofseismic sub-sources at each of the plurality of depths and differenttime delays comprises: applying a weighted summation to the far-fieldsignatures for the plurality of seismic subsources at each of theplurality of depths and different time delays.
 6. The system of claim 1,wherein the removing the source response from the seismic data furthercomprises: removing a receiver ghost from the seismic data.
 7. Thesystem of claim 6, wherein the removing the receiver ghost from theseismic data comprises: measuring pressure and vertical velocitycomponents of the seismic data; and separating up-going and down-goingwavefields using a weighted summation of the measured pressure andvertical velocity components, wherein the down-going wavefields are thereceiver ghost.
 8. At least one computer readable medium with a computerprogram stored thereon, the program having logic operable to cause atleast one programmable computer to perform a method comprising:obtaining seismic data that are acquired using seismic sub-sourcesdisposed in a body of water at a plurality of depths and activated withdifferent time delays; determining far-field signatures for theplurality of seismic sub-sources at each of the plurality of depths;determining a composite ghost-free far-field signature of the seismicsource from the far-field signatures for the plurality of seismicsub-sources at each of the plurality of depths and different timedelays; and removing a source response from the seismic data using thefar-field signatures of the seismic source.
 9. The medium of claim 8,wherein the determining far-field signatures for the plurality ofseismic sub-sources at each of the plurality of depths comprises:determining notional source signatures for the plurality of seismicsub-sources at each of the plurality of depths; and determining afar-field signature from a weighted summation of the notional sourcesignatures.
 10. The medium of claim 8, wherein the determining far-fieldsignatures for the plurality of seismic sub-sources at each of theplurality of depths comprises: measuring the far-field signatures forthe plurality of sub-seismic sources at each of the plurality of depths.11. The medium of claim 8, wherein the determining far-field signaturesfor the plurality of seismic sub-sources at each of the plurality ofdepths comprises: modeling the far-field signatures for the plurality ofseismic sub-sources at each of the plurality of depths.
 12. The mediumof claim 8, wherein the determining the composite ghost-free far-fieldsignature of the seismic source from the far-field signatures for theplurality of seismic sub-sources at each of the plurality of depths anddifferent time delays comprises: applying a weighted summation to thefar-field signatures for the plurality of seismic sub-sources at each ofthe plurality of depths and different time delays.
 13. The medium ofclaim 8 further comprising removing a receiver ghost from the seismicdata.
 14. The medium of claim 13, wherein the removing the receiverghost from the seismic data comprises: measuring pressure and verticalvelocity components of the seismic data; and separating up-going anddown-going wavefields using a weighted summation of the measuredpressure and vertical velocity components.
 15. The system of claim 1,wherein removing the source response from the seismic data using thecomposite ghost-free far-field signature of the seismic source comprisesdeconvolving the composite ghost-free far-field signature from theseismic data.
 16. The medium of claim 8, wherein removing the sourceresponse from the seismic data using the composite ghost-free far-fieldsignature of the seismic source comprises deconvolving the compositeghost-free far-field signature from the seismic data.